Optimal and nearly optimal simulation of multiperiodic time-dependent Hamiltonians

Abstract

Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterizing quantum materials. Recently, a series of quantum algorithms employing block encoding of Hamiltonians have succeeded in providing efficient simulation of time-evolution operators on quantum computers. While time-independent Hamiltonians can be simulated by the quantum eigenvalue transformation (QET) or quantum singular value transformation with the optimal query complexity in time t and desirable accuracy ϵ, generic time-dependent Hamiltonians face at larger query complexity and more complicated oracles due to the difficulty of handling time-dependency. In this paper, we establish a QET-based approach for simulating time-dependent Hamiltonians with multiple time periodicity. Such time-dependent Hamiltonians involve a variety of nonequilibrium systems such as time-periodic systems (Floquet systems) and time-quasiperiodic systems. Overcoming the difficulty of time dependency, our protocol can simulate the dynamics under multiperiodic time-dependent Hamiltonians with optimal and nearly optimal query complexity both in time t and desirable accuracy ϵ, and simple oracles as well as the optimal algorithm for time-independent cases.